一类高阶非齐次线性微分方程亚纯解的零点  

The Zero of Meromorphic Solutions of a Class of Higher Order Nonhomogeneous Linear Differential Equation

作　　者：龙见仁[1] 李晓曼[1] 伍鹏程[1] 

机构地区：[1]贵州师范大学数学与计算机科学学院,贵州贵阳550001

出　　处：《数学的实践与认识》2013年第7期184-189,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11171080);贵州省科学技术厅;贵州师范大学联合科技基金(黔科合J字LKS[2012]12号)

摘　　要：利用亚纯函数的值分布理论研究了下列高阶线性微分方程解的增长性及解的零点增长性,f^((k))+A_(k-1)f^((k-1))+…+A_1f′+A_0f=F(z)其中A_0,A_1,…,A_(k-1),F≠0是亚纯函数.证明了如果A_0以∞为亏值或Borel例外值,那么方程的所有非零解的零点收敛指数均为无穷,至多除去一个例外解,获得的结果推广了以前一些文献的结论.Using theory of the value distribution of meromorphic functions, the problem of the growth and zero of solutions offf^（k）＋Ak-1f^（k-1）＋…＋A1F′＋A0f=F（z）is investigated, where A0,A1,…,Ak-1,F≠0 are meromorphic functions： And under the assumption of certain proper conditions of Ao（z）, oo is a deficient value or Borel exceptional value of A0, we prove a result which the exponents of convergence of the zero-sequence of every nontrivial solutions f（z） of the equation is of infinite, up to remove an exception solution, and improve some results in previous references.

关 键 词：复微分方程 亚纯函数 无穷级 零点收敛指数 

分 类 号：O174.52[理学—数学]